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CN103528634A - Coriolis mass flow meter cloud transmission digital signal processing device and method - Google Patents

Coriolis mass flow meter cloud transmission digital signal processing device and method Download PDF

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CN103528634A
CN103528634A CN201310504736.8A CN201310504736A CN103528634A CN 103528634 A CN103528634 A CN 103528634A CN 201310504736 A CN201310504736 A CN 201310504736A CN 103528634 A CN103528634 A CN 103528634A
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CN103528634B (en
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高瑞
朱邱悦
赵代岳
张岩
朱慧敏
高璐璐
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Shandong University
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Abstract

The invention discloses a Coriolis mass flow meter cloud transmission digital signal processing device and method. The device comprises a Coriolis mass flow meter, wherein the Coriolis mass flow meter is provided with two magnetoelectricity sensors, a driver and a constant flow source, the two magnetoelectricity sensors transmit collected signals to a differential amplification circuit corresponding to the magnetoelectricity sensors, the differential amplification circuit transmits processed signals to a DSP through an AD sampling circuit corresponding to the differential amplification circuit, and the driver is in communicating connection with the DSP through a feedback type digital driving module. According to the method, digital driving is conducted by means of the feedback type non-linear gain control algorithm fast and stably, frequency is tracked with the Newton LMS algorithm in an adaptive mode timely and accurately with the accuracy capable of reaching 0.01%, and the accuracy of calculation of phase difference achieved by means of the DTFT algorithm with a temperature compensation function can reach the 0.02% industrial level. Therefore, the digital signal processing algorithm is a Coriolis mass flow meter signal processing method with high accuracy and strong timeliness.

Description

Cloud transmission digital signal processing device and method for Coriolis mass flowmeter
Technical Field
The invention relates to a cloud transmission digital signal processing device and method for a Coriolis mass flowmeter.
Background
The Coriolis mass flowmeter works based on the fluid vibration principle, the vibration frequency of a pipe is influenced by fluid density and the like, the secondary meter measurement is the phase difference of a synthetic wave, and an analog circuit is sensitive to external noise, so that the measurement accuracy is reduced. In order to improve the accuracy and the anti-interference capability of the coriolis mass flowmeter, a common practice of domestic and foreign research and development institutions and engineers is to apply a digital signal processing algorithm to the signal processing process of the coriolis mass flowmeter. For example, chinese patent CN101832803B uses a synchronous modulation method to calculate the vibration frequency by a zero-crossing comparison method, so as to calculate the phase difference. The method is simple, but the calculation precision is not high. The Beijing university of chemical industry adopts a linear frequency modulation Z transformation algorithm introduced on the basis of DFT to track the frequency of a signal, and adopts a sliding Goertzel algorithm to measure the phase difference of the signal (Linkun, research and implementation of a DSP algorithm of a Coriolis flowmeter, Beijing university of chemical industry, Master academic paper, 2008). The method has high frequency and phase difference precision, but poor real-time performance. The university of combined fertilizer industry proposed a method for enhancing and frequency estimating coriolis flowmeter signals using a normalized lattice IIR adaptive spectral line enhancer, and calculating the time difference of coriolis flowmeter signals using discrete fourier transform with hanning window correction (niwei, research on the coriolis mass flow meter digital signal processing method, university of combined fertilizer industry, doctrine, 2004). The method realizes frequency real-time tracking, but the problem of frequency spectrum leakage exists in phase difference calculation when non-whole period sampling is carried out, and the measurement precision is influenced.
The existing Coriolis mass flowmeter signal processing method has the problems of low precision, low instantaneity and high cost. Therefore, it is urgent to invent a low-cost digital signal processing method with high precision and strong real-time property.
Disclosure of Invention
In order to solve the defects in the prior art, the invention discloses a cloud transmission digital signal processing device and method for a Coriolis mass flowmeter. The method is especially suitable for digital signal processing with fast signal frequency change speed and constantly fluctuating phase difference.
In order to achieve the purpose, the invention adopts the following specific scheme:
a Coriolis mass flowmeter cloud transmission digital signal processing device comprises a Coriolis mass flowmeter, wherein the Coriolis mass flowmeter is provided with two magnetoelectric sensors, a driver and a constant current source, the two magnetoelectric sensors transmit acquired signals to a differential amplification circuit corresponding to the magnetoelectric sensors, and the differential amplification circuit transmits the processed signals to a DSP through an AD sampling circuit corresponding to the differential amplification circuit;
the driver is in communication connection with the DSP through a feedback type digital driving module;
the constant current source is connected with the PT100 and used for providing voltage for the PT100, the PT100 measures external temperature, and the PT100 is connected with the DSP through the AD sampling circuit corresponding to the PT 100. And the constant current source input power supply is connected with the power supply module of the dsp.
The DSP is also connected with the SRAM, the EEPROM, the output of the ePWM, the LCD, the keyboard and the GPS module;
the DSP is also connected with a cloud server through a GPRS module, and the cloud server is connected with the mobile terminal. The mobile terminal is a mobile phone, a computer and the like.
The Coriolis mass flowmeter is a double U-shaped tube Coriolis mass flowmeter.
The GPRS module comprises a SIM300 module.
The device adopts the DSP as a main controller, adopts the feedback type digital driving module to carry out digital driving, utilizes the GPS module to collect the position information of the Coriolis mass flowmeter, adopts the GPRS remote network communication of the SIM300 module, and realizes the data transmission from the DSP to the cloud server and from the cloud server to the mobile network terminal of the parameters obtained by the detection of the Coriolis mass flowmeter. A man-machine interaction function is realized through the LCD and the keyboard, and the ePWM pulse output provides 4-20 mA current output.
The GPRS module can realize remote transmission of measurement data in the cloud server, and the GPS module can realize positioning of the Coriolis mass flowmeter, and can monitor flow data and pipeline damage in real time.
The data received by the cloud server are stored in the database in a classified mode, and are displayed in a webpage mode through a network development technology, so that real-time reading, data comparison and analysis, abnormal condition alarm and the like of monitoring data of the scientific mass flow meter by any network mobile terminal can be realized.
A coriolis mass flowmeter digital signal processing method comprising the steps of:
the method comprises the following steps: the Coriolis mass flowmeter is driven digitally, and a feedback type digital driving module is used for enabling the Coriolis mass flowmeter to start oscillation and maintain a stable working state;
step two: the Coriolis mass flowmeter starts oscillation and maintains a stable working state, then signal preprocessing is carried out, a band-pass IIR digital filter is adopted, digital filtering is carried out on signals obtained by sampling of an AD sampling circuit, and the accuracy of algorithm input data is guaranteed;
step three: self-adaptive frequency tracking, namely extracting an enhanced signal from the sensor vibration signals with phase difference obtained by two paths of AD sampling by using an IIR wave trap, and then self-adaptively tracking the signal frequency by using a Newton LMS algorithm; the IIR wave trap enables the trapped wave frequency to converge to the fundamental frequency of the vibration of the flow tube, all noise outside a narrow frequency band around the fundamental frequency passes through, and the fundamental frequency is solved by combining the parameters of the IIR wave trap with a Newton LMS algorithm;
step four: obtaining the phase difference of the two paths of vibration signals through a discrete time Fourier transform algorithm;
step five: obtaining mass flow after smoothing the phase difference;
step six: and temperature compensation, namely detecting the elastic modulus temperature of a sensitive pipe material of the Coriolis flowmeter, obtaining a compensation coefficient according to the detected temperature, and calculating the compensated instantaneous flow so as to perform digital compensation on the temperature effect.
The specific process of digital driving in the step one is as follows: in the initial driving stage, an initial excitation signal is generated by a DSP module to excite the flow tube of the Coriolis mass flowmeter, when the amplitude detected by a magnetoelectric sensor reaches a given value, a sinusoidal driving signal is synthesized by combining the frequency estimated by a Newton LMS algorithm and the phase estimated by a DTFT algorithm, the amplitude gain of the driving signal at the moment is obtained by utilizing a nonlinear amplitude gain control method, the synthesized sinusoidal signal and the nonlinear amplitude gain are multiplied to obtain the driving signal, a feedback loop is formed, and the flow tube is kept to vibrate nearby the expected amplitude.
The frequency estimation utilizes a Newton LMS algorithm, and the phase estimation utilizes a DTFT algorithm;
the fundamental frequency in the third step is obtained through the following process:
the trap transfer function is as follows:
<math> <mrow> <mi>H</mi> <mrow> <mo>(</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>&rho;wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>&rho;</mi> <mn>2</mn> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>.</mo> </mrow> </math>
wherein, H (z)-1) Is the trap transfer function, w trap factor, ρ trap bandwidth, z-1Is a delay factor. The same reference signs are used in the present application.
Assuming that the input signal is a time-varying signal of a random walk model, the signal function is expressed asWherein A (n) is the signal amplitude, ω (n) is the signal frequency,
Figure BDA0000400668980000033
is the signal phase, e (n) is the random noise signal, n is the discrete time point;
when the parameter w in the trap transfer function is-2 cos ω, the trap output is estimated as:
<math> <mrow> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>&rho;wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>&rho;</mi> <mn>2</mn> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>
wherein,
Figure BDA0000400668980000035
is the estimate of e (n), ω signal angular frequency;
when the value is ρ → 1, then,estimating w by using a Newton LMS algorithm;
the specific process of estimating w by using the Newton LMS algorithm is as follows: the trap output error is
Figure BDA0000400668980000037
Defining a cost function
<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>&epsiv;</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>w</mi> <mo>)</mo> </mrow> </mrow> </math>
Wherein N represents the number of sampling points; epsilon (n, w) trap output error,
wherein the estimation of w
Figure BDA0000400668980000039
Can be expressed as:
Figure BDA00004006689800000310
since ρ tends to 1, according to the formula of the newton LMS algorithm,
Figure BDA00004006689800000311
it can be recursively derived from:
<math> <mrow> <mover> <mi>w</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mover> <mi>w</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>&dtri;</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>
wherein, <math> <mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mrow> <mo>=</mo> <msup> <mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mi>R</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&PartialD;</mo> <mn>2</mn> </msup> <mi>F</mi> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mo>&PartialD;</mo> <mn>2</mn> </msup> <msup> <mi>w</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> </mrow> </mrow> </math>
λ (n) is a forgetting factor, R-1(n) an autocorrelation function, λ (n) ═ λ0λ(n-1)+(1-λ0,λ0,λRespectively as a forgetting factor initial value and a final value, mu (n) is an autocorrelation factor, and v (n) is a discrete gradient operator; newton's LMS is based on the steepest descent method, so the gradient operator is equivalent to the descent rate.
Mu (n) can be obtained by recursion calculation
<math> <mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mo>&dtri;</mo> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
Wherein,
<math> <mrow> <mo>&dtri;</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <mi>w</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>&rho;</mi> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>&rho;wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>&rho;</mi> <mn>2</mn> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>.</mo> </mrow> </math>
here, the bandwidth of each trap is determined by the value of ρ, which is rewritten as ρ (n) if ρ is very close to 1, i.e., the pole is close to the zero, without prior knowledge of the input signal, as defined below:
ρ(n)=ρ0ρ(n-1)+(1-ρ0,
selecting corresponding parameter rho through simulation0,ρThe two values are constant values, and an optimal value, an initial value and a final value are obtained according to signal simulation. Coriolis mass flowmeter signal frequency estimation
Figure BDA0000400668980000046
By the formula
Figure BDA0000400668980000045
And (6) obtaining.
The process for acquiring the phase difference of the two paths of vibration signals in the fourth step is as follows:
the observation signals are two paths of real sinusoidal signals with the same frequency:
s1(t)=A1cos(2πf0t+θ1),
s2(t)=A2cos(2πf0t+θ2).
wherein A is1,A2For different signal amplitudes, f0To the signal frequency, θ1,θ2For two-path signal initial phase, t is sampling time, s1(t),s2(t) is a function of two continuous signals;
at a sampling frequency fs(fs≥2f0) Simultaneously sampling the two paths of signals to obtain a sampling sequence:
s1(n)=A1cos(ωn+θ1),
s2(n)=A2cos(ωn+θ2),n=0,1,...,N-1.
wherein s is1(n)s2(n) is a function of the sampled discrete signals;
let the estimate of ω be
Figure BDA0000400668980000051
Then s1(n) is inDiscrete-time fourier transform:
<math> <mrow> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>A</mi> <mn>1</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&omega;n</mi> <mo>+</mo> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>n</mi> </mrow> </msup> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mfrac> <msub> <mi>A</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mo>[</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mi>&omega;n</mi> <mo>+</mo> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mrow> <mo>(</mo> <mi>&omega;n</mi> <mo>+</mo> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>]</mo> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mover> <mi>&omega;n</mi> <mo>^</mo> </mover> </mrow> </msup> <mo>,</mo> </mrow> </math>
<math> <mrow> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&omega;n</mi> </mrow> </msup> <mo>,</mo> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&omega;n</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&omega;n</mi> </mrow> </msup> <mo>.</mo> </mrow> </math>
wherein S is1,N(omega) is the time when the Nth sampling point of one path of signal is dispersedSignal after inter-Fourier transformation, s1(n) is a discrete signal function after one path of signal sampling, S1,N+1(omega) is a signal obtained by performing discrete time Fourier transform on the N +1 th sampling point of one path of signal,
Figure BDA0000400668980000055
is at the same time
Figure BDA0000400668980000056
Performing discrete time Fourier transform on a signal function;
suppose that
Figure BDA0000400668980000057
Is derived by
Figure BDA0000400668980000058
Wherein, c1,c2,c3,c4Is a derivation process intermediate parameter;
c1=sinα1sinα2cos(α13)+sinα3sinα4cos(α42),
c2=sinα1sinα2sin(α13)-sinα3sinα4sin(α42),
c3=sinα1sinα2sin(α13)+sinα3sinα4sin(α42),
c4=sinα1sinα2cos(α13)-sinα3sinα4cos(α42),
and, α1,α2,α3,α4Is a derivation process intermediate parameter;
<math> <mrow> <msub> <mi>&alpha;</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mn>2</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>+</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mn>3</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mn>4</mn> </msub> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>+</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </math>
Figure BDA00004006689800000510
is S1,N(ω) phase, for s, similarly2(n) presence of
Figure BDA00004006689800000511
<math> <mrow> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>&ap;</mo> <mi>&omega;</mi> <mo>,</mo> <mi>sin</mi> <msub> <mi>&alpha;</mi> <mn>1</mn> </msub> <mo>/</mo> <mi>sin</mi> <msub> <mi>&alpha;</mi> <mn>3</mn> </msub> <mo></mo> <mo>&ap;</mo> <mi>N</mi> <mo>,</mo> <mi>&alpha;</mi> <mo>=</mo> <mi>N</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>,</mo> </mrow> </math> The phase difference Δ θ can be approximately expressed as
Figure BDA0000400668980000061
Wherein m is1,m2,m3,m4To derive process intermediate parameters, phi2Is S2,NThe phase of (ω) and α is the derived process parameter.
<math> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>N</mi> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>N</mi> </mrow> </math>
<math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>N</mi> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>N</mi> <mo>-</mo> <mn>2</mn> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>
<math> <mrow> <msub> <mi>m</mi> <mn>4</mn> </msub> <mo>=</mo> <mi>N</mi> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>N</mi> <mo>+</mo> <mn>2</mn> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>
Calculating the mass flow according to the time difference in the step fivefsTo sample frequency, K is the flow meter constant, and thus the mass flow rate is calculated.
And adopting weighted average to smooth the phase difference in the fifth step.
The digital driving module with feedback control enables the vibrating tube to start vibrating quickly and maintain stable vibration, the influence of external interference on accuracy can be effectively reduced through preprocessing, the digital signal processing algorithm greatly reduces software calculated amount, the Newton LMS self-adaptive algorithm can accurately track signal frequency change in real time, and the DTFT algorithm is fast in convergence and high in accuracy when calculating phase difference, so that the measuring accuracy of mass flow is improved, and the instantaneity is enhanced. The Coriolis mass flowmeter digital signal processing algorithm disclosed by the invention adopts a nonlinear gain control algorithm with feedback to carry out digital driving, is fast and stable, the Newton LMS algorithm is adaptive to tracking frequency in time and accurately, the precision reaches 0.01%, and the phase difference precision calculated by the DTFT algorithm with temperature compensation reaches 0.02% of industrial grade. Therefore, the digital signal processing algorithm is a Coriolis mass flowmeter signal processing method with high precision and strong real-time performance.
The invention has the beneficial effects that:
1. the digital drive overcomes the influence of interference on the analog drive, adopts the driving mode of a feedback loop, can enable the measuring tube to start oscillation rapidly, and keeps a stable working state, thereby providing a foundation for digital signal processing. The acquisition of signal frequency and phase information when synthesizing the driving signal shares the output data of the digital signal processing algorithm, thereby reducing the calculation amount and the occupation of a CPU (central processing unit) and improving the real-time property of driving feedback.
2. The elliptic digital band-pass filter has low order and narrow transition band, can quickly filter most of noise outside a signal fundamental frequency narrow frequency band, and provides accurate input data for the calculation of a digital signal processing algorithm.
3. According to the Newton LMS algorithm based on the IIR wave trap, a Newton gradient operator is introduced on the basis of the traditional LMS algorithm, the descending convergence speed is accelerated, the change of signal frequency can be tracked rapidly and adaptively, and a precondition is provided for phase difference calculation. Meanwhile, the enhanced signal obtained after notching further optimizes the precision of the digital signal processing algorithm.
4. By adopting a recursive DTFT algorithm, only the DTFT of the current point needs to be calculated every time a point is added, and the DTFT of the previous n points is added, so that the calculation amount of the algorithm is greatly reduced, the CPU resource and time are saved, and the phase difference of two paths of sensor signals can be quickly and accurately calculated.
5. The temperature compensation avoids the influence of temperature change on frequency and phase difference calculation, and further improves the calculation precision of the digital signal processing algorithm.
Drawings
FIG. 1 is a schematic diagram of a Coriolis mass flow meter;
FIG. 2 is a connection diagram of a primary meter and a secondary meter;
FIG. 3 is a flow chart of a digital signal processing algorithm;
FIG. 4 is a flow chart of a digitally driven algorithm;
FIG. 5 illustrates a convergence curve of the frequency estimation of the Newton LMS algorithm;
FIG. 6DTFT algorithm calculates the phase difference convergence curve;
FIG. 7 is a hardware block diagram of an algorithm embodiment;
in the figure, 1 parallel U-shaped measuring tube, 2 magnetoelectric sensors B, 3 magnetoelectric sensors A, 4 drivers, 5 transmitters, 6 and 10 core output cables, 7 plugs and connecting cables and 8 sensors.
The specific implementation mode is as follows:
the invention is described in detail below with reference to the accompanying drawings:
as shown in fig. 1, a coriolis mass flowmeter (hereinafter, abbreviated as coriolis mass flowmeter) can directly measure a mass flow rate, and has high measurement accuracy and a wide application prospect. The coriolis flowmeter is classified into a straight tube type and a bent tube type according to its structure. The invention takes a double U-shaped tube Coriolis mass flowmeter as an example for design,
the operating principle of the coriolis flowmeter is described as follows: when fluid flows through the measuring tube of the flowmeter, under the condition of a certain vibration frequency of the measuring tube, phase difference exists between two sine wave signals flowing into the measuring tube and two sine wave signals flowing out of the measuring tube, and the phase difference is in direct proportion to the mass flow of the fluid flowing through the measuring tube. Therefore, the key of the coriolis mass flowmeter is the acquisition of the vibration frequency and the phase difference of the two sensor signals.
As shown in fig. 2, the coriolis mass flowmeter comprises a primary meter and a secondary meter, wherein the primary meter comprises a parallel U-shaped measuring tube 1, a sensor 8, a driver, a temperature sensor and a connecting cable plug, and the sensor comprises a magneto-electric sensor B2 and a magneto-electric sensor A3, wherein the temperature sensor is located at the intersection of the U-shaped tube and the connecting flange. The primary instrument and the secondary instrument are connected by a plug and a connecting cable 7. The secondary instrument mainly comprises a system feedback digital driving module, a signal acquisition module, a signal processing module and an SIM300 module, namely a DSP transmitter. The secondary instrument mainly comprises a system feedback digital driving module, a signal acquisition module and a signal processing module, namely a transmitter, and is used for providing a driving signal for a driver and measuring the frequency and phase difference of a sensor signal. The traditional processing method is based on a signal processing mode of an analog circuit, and is used for amplifying, filtering, shaping, phase demodulating and counting output signals of a sensor and measuring the phase difference.
As shown in fig. 7, a coriolis mass flowmeter digital signal processing device includes a coriolis mass flowmeter, where the coriolis mass flowmeter has two magnetoelectric sensors, a driver, and a constant current source, the two magnetoelectric sensors transmit collected signals to a differential amplification circuit corresponding to the magnetoelectric sensors, and the differential amplification circuit transmits the processed signals to a DSP through an AD sampling circuit corresponding to the differential amplification circuit;
the driver is in communication connection with the DSP through a feedback type digital driving module; the DSP is also connected with the SRAM, the EEPROM, the output of the ePWM, the LCD, the keyboard and the GPS module; the DSP is also connected with a cloud server through a GPRS module, and the cloud server is connected with the mobile terminal. The Coriolis mass flow meter is a double U-shaped tube Coriolis mass flow meter. The GPRS module comprises a SIM300 module.
The device adopts the DSP as a main controller, adopts the feedback type digital driving module to carry out digital driving, utilizes the GPS module to collect the position information of the Coriolis mass flowmeter, adopts the GPRS remote network communication of the SIM300 module, and realizes the data transmission from the DSP to the cloud server and from the cloud server to the mobile network terminal of the parameters obtained by the detection of the Coriolis mass flowmeter. A man-machine interaction function is realized through the LCD and the keyboard, and the ePWM pulse output provides 4-20 mA current output.
As shown in fig. 3, a coriolis mass flowmeter digital signal processing method includes the steps of:
the method comprises the following steps: the Coriolis mass flowmeter is driven digitally, and a feedback type digital driving module is used for enabling the Coriolis mass flowmeter to start oscillation and maintain a stable working state;
step two: the Coriolis mass flowmeter starts oscillation and maintains a stable working state, then signal preprocessing is carried out, a band-pass IIR digital filter is adopted, digital filtering is carried out on signals obtained by sampling of an AD sampling circuit, and the accuracy of algorithm input data is guaranteed;
step three: self-adaptive frequency tracking, namely extracting an enhanced signal from the sensor vibration signals with phase difference obtained by two paths of AD sampling by using an IIR wave trap, and then self-adaptively tracking the signal frequency by using a Newton LMS algorithm; the IIR wave trap enables the trapped wave frequency to converge to the fundamental frequency of the vibration of the flow tube, all noise outside a narrow frequency band around the fundamental frequency passes through, and the fundamental frequency is solved by combining the parameters of the IIR wave trap with a Newton LMS algorithm;
step four: obtaining the phase difference of the two paths of vibration signals through a discrete time Fourier transform algorithm;
step five: obtaining mass flow after smoothing the phase difference;
step six: and temperature compensation, namely detecting the elastic modulus temperature of a sensitive pipe material of the Coriolis flowmeter, obtaining a compensation coefficient according to the detected temperature, and calculating the compensated instantaneous flow so as to perform digital compensation on the temperature effect.
As shown in fig. 4, the specific process of digital driving in step one: in the initial driving stage, an initial excitation signal is generated by a DSP module to excite the flow tube, when the amplitude detected by a magnetoelectric sensor reaches a given value, a sinusoidal driving signal is synthesized by combining frequency estimation and phase estimation, then a nonlinear amplitude gain control method is utilized to obtain the amplitude gain of the driving signal at the moment, the synthesized sinusoidal signal and the nonlinear amplitude gain are multiplied to obtain the driving signal, and a feedback loop is formed to ensure that the flow tube vibrates near the expected amplitude. The phase is obtained by utilizing the feedback type digital driving module to measure, and the amplitude signal controls the driving signal through the nonlinear control algorithm feedback.
The DSP that this device adopted is the TMS320F28335DSP chip of TI company, because the supply voltage of GPRS module is 3.4 ~ 4.5 (typical value is 4.2), when adopting the 5V power supply, need carry out 5V to 4.2V's conversion, this device uses MIC29300 to provide voltage for SIM300, and its output current reaches 3A, can satisfy the requirement of SIM 300.
The GPS module adopts a GS-15C GSP receiver to collect position information, and the precision reaches 5-10 meters. The GPS module has high integration level and is communicated with the DSP through a serial port.
The SIM300 module is internally integrated with a GSM controller, two serial ports, a SIM card interface, two analog audio interfaces and the like. All the hardware interfaces except the antenna interface are connected with the board connector through a 60-pin board, and the pins of the interfaces which cannot be used in transmission are suspended.
The GPRS module works as follows: after the SIM300 module is electrified, a network indicator lamp ON a network LED pin is observed, and when the flicker frequency of the network indicator lamp is changed to 64ms ON/3000ms OFF, the module is connected to a GPRS network at the moment, and a low pulse which is more than 1500ms is output to a PWKEY pin through a DSPF28335 pin to start the SIM300 module. The inside of the SIM300 is integrated with a TCP/IP protocol, and the DSPF28335 sends an AT instruction to the SIM300 through a serial port, so that the SIM300 can be controlled to realize a data transmission function.
The cloud server is configured as a fixed IP database system, and the SIM300 accesses a certain set port (for example, 80 ports) of the cloud server through the GPRS, thereby performing communication between the GPRS module and the cloud server. The cloud server stores the received monitoring data into a database according to data types, wherein the data types mainly comprise mass flow, temperature, GPS positioning position, acquisition time and the like. And the contents of the database are displayed in a webpage form by utilizing a network development technology, so that real-time positioning, real-time detection and real-time query are realized. Therefore, any mobile network terminal can access the cloud space through the website, and the working state of the Coriolis flowmeter is observed on line in real time.
The CPUTIMER0 timer interrupt is utilized to obtain 1s accumulated flow, and the accumulated flow is stored in the external EEPROM.
The PWM output function obtains a pulse signal with flow information by one path of PWM comparison function in the ePWM of the DSP.
The man-machine interface consists of an LCD and a keyboard, and realizes specific functions by utilizing a DSP multifunctional multiplexing GPIO port. The LCD displays the measurement results of instantaneous flow, cumulative flow, temperature, etc. The keyboard is mainly used for setting the meter coefficient.
The initial sinusoidal excitation signal is provided by the DSP, the signal amplitude is changed from small to large, and when the vibration amplitude reaches a given value, the signal frequency and the phase are estimated by utilizing the Newton LMS notch algorithm and the DTFT algorithm, so that the sinusoidal driving signal is synthesized. Then, an amplitude gain is determined by a difference from a given amplitude according to the change in the amplitude of vibration. And finally, taking the product of the synthesized sine wave and the gain as a feedback driving signal to keep the vibration amplitude of the flow tube in a stable working state.
After the flow tube works stably in a vibrating mode, two paths of signals of the magnetoelectric sensors are acquired by two paths of AD, the signals are transmitted to the temporary array of the internal storage through the multichannel buffer serial port Mcbsp, DMA receiving interruption is generated after the temporary array is fully placed, and two temporary array data are transferred to the SRAM buffer array expanded externally.
And according to the DSP operation speed, 500 points of data are taken every time, and when the signal amplitude is larger than a set value, an algorithm module is called. Preprocessing the data, designing a Chebyshev band-pass filter according to the parameters of the flow tube, and storing the filtered data in an externally-expanded SRAM array.
And (4) the filtered data in the temporary array enters a Newton LMS notch algorithm module, and on one hand, the Newton LMS algorithm is used for self-adaptively estimating the fundamental frequencies of the two paths of signals. In order to ensure the frequency precision, the fundamental frequency is averaged, a fluctuation range is set, when the fluctuation amplitude is larger than a set value, the frequency is not updated, otherwise, the frequency is updated, and the frequency value is stored in an external expansion array. On the other hand, the two paths of signals pass through the wave trap and then are enhanced signals for filtering noise, the enhanced signals are stored, and accurate input data are provided for phase difference calculation.
When a DTFT algorithm is called to obtain a phase difference of the enhanced signal, the DTFT is carried out on the enhanced signal, then the real part and the imaginary part of the signal are respectively stored in two external expansion groups according to the calculation characteristics of the algorithm, so that a phase difference of two paths of signals is obtained, then the phase difference is smoothed, a time difference is obtained by combining frequency values, and then instantaneous flow is obtained. The meter coefficients are stored in an externally extended EEPROM.
The method comprises the steps of collecting signals of a temperature sensor, entering a DSP (digital signal processor) through a Serial Peripheral Interface (SPI) to be converted into temperature values, obtaining corresponding temperature compensation coefficients according to the material of a flowmeter, and carrying out temperature compensation on instantaneous flow.
Temperature compensation: the elastic modulus of the sensitive tube material of the Coriolis flowmeter changes along with the temperature change, the temperature can be detected timely, the compensation coefficient is obtained according to the temperature, and the compensated instantaneous flow is calculated, so that the temperature effect is digitally compensated.
For single-phase flow signals, the improvement of calculation precision and the expansion of the lower limit of the measuring range are the targets of a Coriolis mass flowmeter digital signal processing algorithm. Especially for small-flow signals, the signals are weak, the signal-to-noise ratio is low, and the phase difference obtained by DTFT calculation has large fluctuation, so that the phase difference needs to be smoothed by adopting weighted average. But the sudden change of the flow can generate a measurement error, a phase difference limit value is set for the purpose, and if the calculation results of continuous 10 phase differences exceed the limit value, the average value of the sum of the 10 phase difference values is taken as the current phase difference, so that the flow change reaction speed is accelerated.
Respectively calculating two paths of signals in the process of the DTFT recursive algorithm
Figure BDA0000400668980000101
The phase difference delta theta of the two paths of signals can be obtained after the phase subtraction of the DTFT, which is the basic principle of the DTFT recursion algorithm for measuring the phase difference.
And continuously adjusting parameters of the wave trap according to the change of the signal characteristics after the convergence of the Newton LMS self-adaptive algorithm, and tracking the change of the vibration frequency. And the zero point is fixed on the unit circle by adopting an IIR wave trap constrained by a zero point and is positioned at the trap frequency, and the pole is arranged in the unit circle and has the same angle with the zero point.
Because the industrial field noise is more than 5KHz, the filtering effect can be achieved by adopting a simple band-pass filter under high sampling frequency.
In general, when the signal-to-noise ratio is not particularly low, the signal frequency value obtained by convergence of the adaptive lattice type trap is very close to the true value, i.e. it can be considered that
Figure BDA0000400668980000112
To this patent simulation experiment, in the simulation (as shown in fig. 5), sampling parameters: signal frequency f =200hz, and sampling frequency fs = 2000. At the moment that the frequency is calculated to be less than 100 points, the Newton LMS algorithm achieves convergence, the frequency tracking is fast and accurate, and the precision is 0.01 percent.
The DTFT algorithm can quickly and accurately calculate the phase difference of the two sensor signals. In the simulation (as shown in fig. 6), the phase difference parameters are: phasediff =0.01,. At the time of phase difference calculation about 300 points, the phase difference has already reached convergence, and the precision is about 0.02%.
The experiment also simulates 5 phases in the interval from 0.01 to 0.4 degrees, and the average value of 5 measurement results is taken for each phase difference, and the calculation precision is shown in table 1.
TABLE 1DTFT Algorithm phase difference calculation simulation data
Figure BDA0000400668980000111

Claims (10)

1. A Coriolis mass flowmeter cloud transmission digital signal processing device is characterized by comprising a Coriolis mass flowmeter, wherein the Coriolis mass flowmeter is provided with two magnetoelectric sensors, a driver and a constant current source, the two magnetoelectric sensors transmit acquired signals to a differential amplification circuit corresponding to the magnetoelectric sensors, and the differential amplification circuit transmits the processed signals to a DSP through an AD sampling circuit corresponding to the differential amplification circuit;
the driver is in communication connection with the DSP through a feedback type digital driving module;
the constant current source is connected with the PT100, the constant current source is used for providing voltage for the PT100, the PT100 measures the external temperature, and the PT100 is connected with the DSP through the AD sampling circuit corresponding to the PT 100;
the DSP is also connected with a cloud server through a GPRS module, and the cloud server is connected with the mobile terminal.
2. The coriolis mass flowmeter cloud transfer digital signal processing device of claim 1, wherein the DSP is further connected to the output of the SRAM, the EEPROM, the ePWM, the LCD, the keyboard, and the GPS module.
3. The coriolis mass flowmeter cloud transfer digital signal processing device of claim 1, wherein the coriolis mass flowmeter is a dual U-tube coriolis mass flowmeter.
4. The coriolis mass flowmeter cloud transfer digital signal processing device of claim 1, wherein the GPRS module comprises a SIM300 module.
5. The digital signal processing method for the cloud transmission digital signal processing device of the coriolis mass flowmeter as set forth in claim 1, comprising the steps of:
the method comprises the following steps: the Coriolis mass flowmeter is driven digitally, and a feedback type digital driving module is used for enabling the Coriolis mass flowmeter to start oscillation and maintain a stable working state;
step two: the Coriolis mass flowmeter starts oscillation and maintains a stable working state, then signal preprocessing is carried out, a band-pass IIR digital filter is adopted, digital filtering is carried out on signals obtained by sampling of an AD sampling circuit, and the accuracy of algorithm input data is guaranteed;
step three: self-adaptive frequency tracking, namely extracting an enhanced signal from the sensor vibration signals with phase difference obtained by two paths of AD sampling by using an IIR wave trap, and then self-adaptively tracking the signal frequency by using a Newton LMS algorithm; the IIR wave trap enables the trapped wave frequency to converge to the fundamental frequency of the vibration of the flow tube, all noise outside a narrow frequency band around the fundamental frequency passes through, and the fundamental frequency is solved by combining the parameters of the IIR wave trap with a Newton LMS algorithm;
step four: obtaining the phase difference of the two paths of vibration signals through a discrete time Fourier transform algorithm;
step five: obtaining mass flow after smoothing the phase difference;
step six: and temperature compensation, namely detecting the elastic modulus temperature of a sensitive pipe material of the Coriolis flowmeter, obtaining a compensation coefficient according to the detected temperature, and calculating the compensated instantaneous flow so as to perform digital compensation on the temperature effect.
6. The method of claim 5, wherein the specific process of digital driving in step one: in the initial driving stage, an initial excitation signal is generated by a DSP module to excite the flow tube of the Coriolis mass flowmeter, when the amplitude detected by a magnetoelectric sensor reaches a given value, a sinusoidal driving signal is synthesized by combining the frequency estimated by a Newton LMS algorithm and the phase estimated by a DTFT algorithm, the amplitude gain of the driving signal at the moment is obtained by utilizing a nonlinear amplitude gain control method, the synthesized sinusoidal signal and the nonlinear amplitude gain are multiplied to obtain the driving signal, a feedback loop is formed, and the flow tube is kept to vibrate nearby the expected amplitude.
7. The method as claimed in claim 5, wherein the fundamental frequency in the third step is obtained by:
the trap transfer function is as follows:
<math> <mrow> <mi>H</mi> <mrow> <mo>(</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>&rho;wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>&rho;</mi> <mn>2</mn> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>.</mo> </mrow> </math>
wherein, H (z)-1) Is the trap transfer function, w trap factor, ρ trap bandwidth, z-1In order to be a delay factor, the delay factor,
assuming that the input signal is a time-varying signal of a random walk model, the signal function is expressed asWherein A (n) is the signal amplitude, ω (n) is the signal frequency,
Figure FDA00004006689700000213
is the signal phase, e (n) is the random noise signal, n is the discrete time point;
when the parameter w in the trap transfer function is-2 cos ω, the trap output is estimated as:
<math> <mrow> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>&rho;wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>&rho;</mi> <mn>2</mn> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mi>x</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>
wherein,
Figure FDA0000400668970000023
is the estimate of e (n), ω signal angular frequency;
when the value is ρ → 1, then,
Figure FDA0000400668970000024
estimating w by using a Newton LMS algorithm;
the specific process of estimating w by using the Newton LMS algorithm is as follows: the trap output error is
Figure FDA0000400668970000025
Defining a cost function
<math> <mrow> <mi>F</mi> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mn>1</mn> <mi>N</mi> </mfrac> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msup> <mi>&epsiv;</mi> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>,</mo> <mi>w</mi> <mo>)</mo> </mrow> </mrow> </math>
Wherein N represents the number of sampling points;
wherein the estimation of w
Figure FDA0000400668970000027
Can be expressed as:
Figure FDA0000400668970000028
since ρ tends to 1, according to the formula of the newton LMS algorithm,
Figure FDA0000400668970000029
it can be recursively derived from:
<math> <mrow> <mover> <mi>w</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>=</mo> <mover> <mi>w</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>&dtri;</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> </math>
wherein, <math> <mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mrow> <mo>=</mo> <msup> <mrow> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <mi>R</mi> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>-</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>)</mo> </mrow> <msup> <mrow> <mo>(</mo> <mfrac> <mrow> <msup> <mo>&PartialD;</mo> <mn>2</mn> </msup> <mi>F</mi> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msup> <mo>&PartialD;</mo> <mn>2</mn> </msup> <msup> <mi>w</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo>)</mo> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>,</mo> </mrow> </mrow> </math>
λ (n) is a forgetting factor, R-1(n) autocorrelation function λ (n) ═ λ0λ(n-1)+(1-λ0,λ0λForgetting factor initial and final values, μ (n) is an autocorrelation factor, and ^ (n) is a discrete gradient operator; newton LMS is based on the steepest descent method, so the gradient operator is equivalent to the descent rate,
mu (n) can be obtained by recursion calculation
<math> <mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>+</mo> <msup> <mo>&dtri;</mo> <mn>2</mn> </msup> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mi>&mu;</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> </mfrac> <mo>,</mo> </mrow> </math>
Wherein,
<math> <mrow> <mo>&dtri;</mo> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mo>&PartialD;</mo> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&PartialD;</mo> <mi>w</mi> </mrow> </mfrac> <mo>=</mo> <mfrac> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> <mo>-</mo> <mi>&rho;</mi> <mover> <mi>e</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> <mo>)</mo> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <msup> <mi>&rho;wz</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>&rho;</mi> <mn>2</mn> </msup> <msup> <mi>z</mi> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> </mrow> </mfrac> <mo>.</mo> </mrow> </math>
here, the bandwidth of each trap is determined by the value of ρ, which is rewritten as ρ (n) if ρ is very close to 1, i.e., the pole is close to the zero, without prior knowledge of the input signal, as defined below:
ρ(n)=ρ0ρ(n-1)+(1-ρ0,
selecting corresponding parameter rho through simulation0,ρValue of (1), Coriolis mass flowmeter signal frequency
Figure FDA0000400668970000033
By the formula <math> <mrow> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <msup> <mi>cos</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mrow> <mo>(</mo> <mo>-</mo> <mover> <mi>w</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>n</mi> <mo>/</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>)</mo> </mrow> </mrow> </math> And (6) obtaining.
8. The method as claimed in claim 5, wherein the step four includes obtaining the phase difference between the two vibration signals by:
the observation signals are two paths of real sinusoidal signals with the same frequency:
s1(t)=A1cos(2πf0t+θ1)
s2(t)=A2cos(2πf0t+θ2)
wherein A is1,A2For different signal amplitudes, f0To the signal frequency, θ1,θ2For two-path signal initial phase, t is sampling time, s1(t),s2(t) is a function of two continuous signals;
at a sampling frequency fs(fs≥2f0) Simultaneously sampling the two paths of signals to obtain a sampling sequence:
s1(n)=A1cos(ωn+θ1),
s2(n)=A2cos(ωn+θ2),n=0,1,...,N-1.
wherein s is1(n)s2(n) is a function of the sampled discrete signals;
let the estimate of ω be
Figure FDA0000400668970000035
Then s1(n) is in
Figure FDA0000400668970000036
Discrete-time fourier transform:
<math> <mrow> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>A</mi> <mn>1</mn> </msub> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&omega;n</mi> <mo>+</mo> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>n</mi> </mrow> </msup> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mfrac> <msub> <mi>A</mi> <mn>1</mn> </msub> <mn>2</mn> </mfrac> <mo>[</mo> <msup> <mi>e</mi> <mrow> <mi>j</mi> <mrow> <mo>(</mo> <mi>&omega;n</mi> <mo>+</mo> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>+</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mrow> <mo>(</mo> <mi>&omega;n</mi> <mo>+</mo> <msub> <mi>&theta;</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> </mrow> </msup> <mo>]</mo> <mo>&CenterDot;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j</mi> <mover> <mi>&omega;n</mi> <mo>^</mo> </mover> </mrow> </msup> <mo>,</mo> </mrow> </math>
<math> <mrow> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&omega;n</mi> </mrow> </msup> <mo>,</mo> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&Sigma;</mi> <mrow> <mi>n</mi> <mo>=</mo> <mn>0</mn> </mrow> <mi>N</mi> </munderover> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&omega;n</mi> </mrow> </msup> <mo>=</mo> <msub> <mi>S</mi> <mrow> <mn>1</mn> <mo>,</mo> <mi>N</mi> </mrow> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>+</mo> <msub> <mi>s</mi> <mn>1</mn> </msub> <mrow> <mo>(</mo> <mi>N</mi> <mo>)</mo> </mrow> <mo>*</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <mi>j&omega;n</mi> </mrow> </msup> <mo>.</mo> </mrow> </math>
wherein S is1,N(omega) is a signal s obtained by performing discrete time Fourier transform on an Nth sampling point of one path of signal1(n) is a discrete signal function after one path of signal sampling, S1,N+1(omega) is a signal obtained by performing discrete time Fourier transform on the N +1 th sampling point of one path of signal,
Figure FDA0000400668970000043
is at the same time
Figure FDA0000400668970000044
Performing discrete time Fourier transform on a signal function;
suppose that
Figure FDA0000400668970000045
Is derived by
Wherein, c1,c2,c3,c4Is a derivation process intermediate parameter;
c1=sinα1sinα2cos(α13)+sinα3sinα4cos(α42),
c2=sinα1sinα2sin(α13)-sinα3sinα4sin(α42),
c3=sinα1sinα2sin(α13)+sinα3sinα4sin(α42),
c4=sinα1sinα2cos(α13)-sinα3sinα4cos(α42),
and, α1,α2,α3,α4Is a derivation process intermediate parameter;
<math> <mrow> <msub> <mi>&alpha;</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mn>2</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>+</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mn>3</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> <msub> <mi>&alpha;</mi> <mn>4</mn> </msub> <mo>=</mo> <mi>N</mi> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>+</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>/</mo> <mn>2</mn> <mo>,</mo> </mrow> </math>
Figure FDA00004006689700000412
is S1,N(ω) phase, for s, similarly2(n) presence of
Figure FDA0000400668970000048
<math> <mrow> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>&ap;</mo> <mi>&omega;</mi> <mo>,</mo> <mi>sin</mi> <msub> <mi>&alpha;</mi> <mn>1</mn> </msub> <mo>/</mo> <mi>sin</mi> <msub> <mi>&alpha;</mi> <mn>3</mn> </msub> <mo></mo> <mo>&ap;</mo> <mi>N</mi> <mo>,</mo> <mi>&alpha;</mi> <mo>=</mo> <mi>N</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>,</mo> </mrow> </math> The phase difference Δ θ can be approximately expressed as
Figure FDA00004006689700000410
Wherein m is1,m2,m3,m4To derive process intermediate parameters, phi2Is S2,NThe phase of (omega) is such that,
<math> <mrow> <msub> <mi>m</mi> <mn>1</mn> </msub> <mo>=</mo> <mi>N</mi> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>N</mi> </mrow> </math>
<math> <mrow> <msub> <mi>M</mi> <mn>2</mn> </msub> <mo>=</mo> <mi>N</mi> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>N</mi> <mo>-</mo> <mn>2</mn> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>
<math> <mrow> <msub> <mi>m</mi> <mn>3</mn> </msub> <mo>=</mo> <mn>2</mn> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mo>.</mo> </mrow> </math>
<math> <mrow> <msub> <mi>m</mi> <mn>4</mn> </msub> <mo>=</mo> <mi>N</mi> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>+</mo> <msup> <mrow> <mo>(</mo> <mi>sin</mi> <mi>&alpha;</mi> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>/</mo> <mi>N</mi> <mo>+</mo> <mn>2</mn> <mi>sin</mi> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mi>sin</mi> <mi></mi> <mi>&alpha;</mi> <mi>cos</mi> <mrow> <mo>(</mo> <mi>&alpha;</mi> <mo>-</mo> <mover> <mi>&omega;</mi> <mo>^</mo> </mover> <mo>)</mo> </mrow> </mrow> </math>
9. the method as set forth in claim 5, wherein the mass flow rate calculation in said step five is based on the time difference
Figure FDA0000400668970000055
fsTo sample frequency, K is the flow meter constant, and thus the mass flow rate is calculated.
10. The method as claimed in claim 5, wherein the phase difference smoothing in step five is performed by weighted averaging.
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